Biodynamic farming is an older, more philosophical sibling to organic. Developed by Rudolf Steiner in the 1920s, it treats the farm as a closed, self-sustaining ecosystem and prescribes specific practices tied to cosmic cycles (planting by the moon, for instance) in addition to organic-adjacent restrictions on synthetic inputs.
Certification is through Demeter, an international body older than USDA Organic. Practically, certified biodynamic is rarer than organic; you see it most often in wine, olive oil, and some specialty produce.